# Thermodynamics

Mechanics

Oct 28, 2013 (4 years and 6 months ago)

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Modern Methods in Heterogeneous Catalysis

F.C. Jentoft, November 22, 2002

Outline

1.
Motivation

2.

3.
Volumetric System

Calibration of volume

4.
Calorimeter

Calibration of calorimeter

Measurement of heat signal

Lewis
-
sites

coordinatively unsaturated (cus) metal cations (acidic)

oxygen anions (basic)

Questions:

Type?

Number / density?

„Strength“ (interaction with a certain molecule)?

Motivation: Surface Sites

Brønsted
-
sites

OH
-
groups (
acidic
/ basic)

Metal Sites

IR, XPS, NMR,

UV/Vis...

shift of bands

(probe/surface)

desorption
T

TDS/TPD

H

calorimetry

+ NH
3

Probing Surface Sites by
Chemisorption

Physisorption (e.g. N
2
) yields geometric surface area

A

B

C

Specific adsorption / chemisorption gives information
about a particular type of site which depends on the type
of probe used

A, B can be distinguished,

B and C can maybe distinguished

A

B

C

A probe may chemisorb on different sites under
production of different heats of adsorption

If all sites are covered at once, the evolved heat will be an
integral heat

if the number of adsorbed molecules is known, an average /
mean heat of adsorption can be calculated

A general concept: example dissolution

“first”, “last” heat of dissolution = differential heats

Sites can be covered step by step, e.g.

1.

2.

3.

Differential heats of adsorption as a function of coverage
can be determined

The sorptive must be introduced stepwise, i.e. at
constant temperature, the pressure is increased slowly

determined (isotherm)

For each adsorption step, the evolved heat must be
determined

The differential heat can then be determined by division
of evolved heat through number of molecules adsorbed
in a particular step

via the pressure decrease through the adsorption (no
change in number of molecules in system during

via increase in sample weight

via the evolved heat (if heat of adsorption known and
constant)

spectroscopically (if extinction coefficient of adsorbed
species known)

Pressure Decrease Method

A known number of molecules of the sorptive is
introduced into the sample cell

The sorptive is distributed into three partitions:

the equilibrium pressure with sample is compared to the
equilibrium pressure without sample at equal number of
sorptive molecules in the cell

from the pressure difference the number of adsorbed
molecules can be calculated

Dosing a Known Amount of Gas

A known number of molecules of the sorptive is
introduced into the sample cell

If we know the volume, temperature and pressure, we
can calculate the number of gas molecules

Need V, T, p

The Dosing Volume

vacuum

gas in

DOSING VOLUME

p, T can be easily measured

V needs to be determined

pressure gauge dosing system

Volume Calibration

A volume can be measured by determining the amount
of liquid that it can take up

a) gravimetrically: weight / density of liquid

b) volumetrically: add liquid from a burette

An unknown volume of any shape can then be
determined through expansion from gas (an ideal gas
that does not stick much to the walls) from one volume to
the other and pressure measurement before and after
the equilibration

Calibrating the Dosing Volume

vacuum

gas in

pressure gauge dosing system

DOSING VOLUME V
Dos

CALIBRATION VOLUME V
Cal

fill
V
Cal

and
V
Dos
, same pressure

close valve between
V
Cal

and

V
Dos

set pressure in
V
dos

to p
Dos

open valve, equilibrate

Calibrating the Dosing Volume

vacuum

gas in

pressure gauge dosing system

DOSING VOLUME

CALIBRATION VOLUME

Initial situation:

After opening valve:

n, T are constant

Example Data

It is important that the entire system is at the same
constant temperature!

Calibration and Dosing System

Determining the Dosed Amount

vacuum

gas in

sample cell

pressure gauge dosing system

DOSING VOLUME

CELL VOLUME

CALIBRATION VOLUME

The Cell

Total Number of Molecules in

Sample Cell

Total number of molecules accumulated in cell

i.e. the sum of

the number of molecules already in the cell

the number of molecules introduced in the i
th

step

Molecules are in the gas phase but also adsorbed
on the wall surface

Only the gas phase molecules contribute to the
measured pressure

The number of molecules adsorbed on the walls
depends on the pressure

Volumetric
-
Barometric System

vacuum

gas in

sample cell

pressure gauge dosing system

DOSING VOLUME

CELL VOLUME

CALIBRATION VOLUME

pressure gauge sample cell

sample
, the relation between pressure
and number of molecules in the
sample cell would be given by the
ideal gas law

Measure the pressure in the cell as a function of the total
number of molecules introduced into the cell

With wall adsorption and with or without a sample
, the
relation between number of molecules in the gas phase + on
the walls and the pressure can be written as a polynomial
expression

Without a sample
, the coefficients can be determined

Example Blank Measurement

Nr

p

Dos,bef

/

mbar

p

Dos,aft

/

mbar

p

SC,i

/

mbar

n

int,i

/

µmol

n

SCt

o

t,i

/

µmol

1

9,682

9,674

0,007

0,04

0,04

2

9,653

9,641

0,026

0,06

0,10

3

9,607

9,591

0,054

0,08

0,18

4

9,562

9,544

0,081

0,09

0,27

5

9,499

9,481

0,117

0,09

0,36

6

9,442

9,428

0,147

0,07

0,43

7

9,392

9,371

0,181

0,11

0,54

9

9,230

9,195

0,283

0,18

0,72

10

9,128

9,091

0,344

0,19

0,91

11

9,024

8,988

0,403

0,19

1,10

13

8,814

8,758

0,537

0,29

1,39

14

8,644

8,582

0,640

0,32

1,71

15

8,466

8,386

0,755

0,42

2,13

16

8,209

8,122

0,909

0,45

2,58

17

7,783

7,612

1,208

0,90

3,48

19

6,672

6,487

1,870

0,97

3,45

20

5,893

5,526

2,436

1,93

5,38

21

4,477

4,041

3,314

2,30

7,68

22

9,146

8,409

4,056

3,88

11,56

The adsorption of isobutane on the walls is insignificant

Total number of molecules in
sample cell after the i
th

step

Total number of molecules in
sample cell after the (i+1)
th

step

The difference in number of molecules between i
th

and (i+1)
th

step is the number of molecules introduced in the (i+1)
th

step

T number of molecules adsorbed in the (i+1)
th

step is then

The total number of molecules adsorbed after (i+1) steps is

Raw Data Pressure

The Calorimetric Element

The sample cell is placed into
a calorimeter element

The cell is surrounded by a
400 thermocouples in series

Thermopile has 2 functions:
transfers heat

generates signal

Heat and Heat Flow

The heat produced by the
reaction is consumed by two
processes

1. Increase of the temperature
of the sample cell

2. Once there is a temperature
surrounding block, heat flow
through the thermopile

Power

The power P [W] necessary to heat the cell by d

is
proportional to the heat capacity C [J/K] of the cell

The heat flow

[power] is proportional to the


between cell and block and to
the
thermal conductance G [W/K] (thermischer Leitwert)

Power Balance and Signal

Total thermal power of cell

The electrical signal is proportional to
the temperature
difference

The relation between power and electrical signal is then

The Tian Equation

G [W/K] is constant and if C [J/K] can be
considered constant, then C/G is a
constant with units of time

The Tian equation shows that the power is not
proportional to the temperature difference, the power is
delayed with respect to the signal U produced by the cell

Reference Cell

Setup according to

Tian and Calvet

Setup according to

Petit

Complete System

vacuum

gas in

sample cell

pressure gauge dosing system

DOSING VOLUME

CELL VOLUME

CALIBRATION VOLUME

pressure gauge sample cell

vacuum

reference cell

The Calorimeter

Calculation of Evolved Heat

If heat is released in the cell for a limited period
of time, e.g. through adsorption, then a signal
with an exponential decrease is obtained for U

The integral under the curve is proportional to
the evolved heat

A: area under curve [Vs]

f: calibration factor [J/(Vs)]

Calibration Procedure

The calorimeter can be calibrated in two different ways,
easily achieved by using an Ohm resistance:

1. Constant power

2. Produce a certain amount of heat, Q = U*I*t

Disadvantage of the electrical calibration: heat transfer
through wiring!

Calibration by chemical reaction

Calibration Data

The calibration factor is temperature dependent

Check for linearity

Calibration Data

Raw Data:

Equilibrium Pressure and Thermosignal

Sulfated Zirconia

Heteropolyacids

H
3
PW
12
O
40

* x H
2
O reaction with ammonia

Literature

A. Auroux “Thermal Methods: Calorimetry, Differential
Thermal Analysis, and Thermogravimetry” in “Catalyst
characterization: physical techniques for solid materials”,
Eds. B. Imelik, J.C. Vedrine, Plenum Pr., New York 1994

FHI 28 I 57

E. Calvet, H. Prat, H.A. Skinner “Recent progress in
microcalorimetry”, Pergamon Pr., Oxford1963

FHI 6 Z 17